Elementary Proof of Petz–Hasegawa Theorem

Abstract

We give an elementary proof of the following important result first stated by Petz–Hasegawa:

$$\begin{array}{ll}f_{p}(t)= p (1-p) \frac{(t-1)^2}{(t^{p}-1) (t^{1-p}-1)}\; {\rm is\; an\; operator\; monotone\; function\; for }\; -1 \le p \le 2\end{array}$$

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